In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational (...) axiomatization. A proper FA is an algebra of relations where the fork is induced by an injective operation coding pair formation. In contrast to RAs, FAs are representable by proper ones and their equational theory has the expressive power of full first-order logic. A square semantics (the set of arrows is ᵎ x ᵎ for some set ᵎ) for arrow logic was defined by Y. Venema. Due to the negative results about the finite axiomatizability of representable RAs, Venema provided a non-orthodox finite axiomatization for arrow logic by adding a new rule governing the applications of a difference operator. We address here the question of extending the type of relational structures to define orthodox axiomatizations for the class of squares. Given the connections between this problem and the finitization problem addressed by I. Németi, we suspect that this cannot be done by using only logical operations. The modal version of the FA equations provides an orthodox axiomatization for FAL which is complete in view of the representability of FAs. Here we review this result and carry it further to prove that this orthodox axiomatization for FAL also axiomatizes the class of fork squares. (shrink)

We compare fork arrow logic, an extension of arrow logic, and its natural first-order counterpart (the correspondence language) and show that both have the same expressive power. Arrow logic is a modal logic for reasoning about arrow structures, its expressive power is limited to a bounded fragment of first-order logic. Fork arrow logic is obtained by adding to arrow logic the fork modality (related to parallelism and synchronization). As a result, fork arrow logic attains the expressive power of its first-order (...) correspondence language, so both can express the same input–output behavior of processes. (shrink)

Rapid individual cognitive phenotyping holds the potential to revolutionize domains as wide‐ranging as personalized learning, employment practices, and precision psychiatry. Going beyond limitations imposed by traditional lab‐based experiments, new efforts have been underway toward greater ecological validity and participant diversity to capture the full range of individual differences in cognitive abilities and behaviors across the general population. Building on this, we developed Skill Lab, a novel game‐based tool that simultaneously assesses a broad suite of cognitive abilities while providing an engaging (...) narrative. Skill Lab consists of six mini‐games as well as 14 established cognitive ability tasks. Using a popular citizen science platform (N = 10,725), we conducted a comprehensive validation in the wild of a game‐based cognitive assessment suite. Based on the game and validation task data, we constructed reliable models to simultaneously predict eight cognitive abilities based on the users’ in‐game behavior. Follow‐up validation tests revealed that the models can discriminate nuances contained within each separate cognitive ability as well as capture a shared main factor of generalized cognitive ability. Our game‐based measures are five times faster to complete than the equivalent task‐based measures and replicate previous findings on the decline of certain cognitive abilities with age in our large cross‐sectional population sample (N = 6369). Taken together, our results demonstrate the feasibility of rapid in‐the‐wild systematic assessment of cognitive abilities as a promising first step toward population‐scale benchmarking and individualized mental health diagnostics. (shrink)

We investigate the possibility to characterize (multi) functions that are Σ b i -definable with small i (i = 1, 2, 3) in fragments of bounded arithmetic T 2 in terms of natural search problems defined over polynomial-time structures. We obtain the following results: (1) A reformulation of known characterizations of (multi)functions that are Σ b 1 - and Σ b 2 -definable in the theories S 1 2 and T 1 2 . (2) New characterizations of (multi)functions that are (...) Σ b 2 - and Σ b 3 -definable in the theory T 2 2 . (3) A new non-conservation result: the theory T 2 2 (α) is not ∀Σ b 1 (α)-conservative over the theory S 2 2 (α). To prove that the theory T 2 2 (α) is not ∀Σ b 1 (α)-conservative over the theory S 2 2 (α), we present two examples of a Σ b 1 (α)-principle separating the two theories: (a) the weak pigeonhole principle WPHP (a 2 , f, g) formalizing that no function f is a bijection between a 2 and a with the inverse g, (b) the iteration principle Iter (a, R, f) formalizing that no function f defined on a strict partial order ( $\{0,\dots,a\}$ , R) can have increasing iterates. (shrink)

This collection of essays, written on four continents by scientists, philosophers and humanists, was initially presented to Karl R. Popper on his sixtieth birthday as a token of critical admiration and in recognition of his work. But the volume also stands on its own as a remarkable series of statements utilizing Popper's critical vision in the study of philosophy proper, logic, mathematics, science as method and theory, and finally to the study of society and history. What is remarkable is that (...) Popper worked in all of these areas, not in a cursory or discursive way, but with the utmost clarity and rigor.. The core position of this volume and its contributors is that the progress of knowledge is not a linear accumulation of definitive acquisitions but a zigzagging process in which counterexamples and unfavorable evidence ruin generalizations and prompt the invention of more comprehensive and sometimes deeper generalizations, to be criticized in their turn. A critical approach to problems, procedures, and results in every field of inquiry is therefore a necessary condition for the continuance of progress. The title of this volume then is, in a sense, an homage to Popper's critical rationalism and critical empiricism. The essays are a tribute to his unceasing and uncompromising quest, not for final certainty, but for closer truth and increased clarity. Among the contributors are outstanding figures in philosophy and the exact sciences in their own right, including Herbert Feigl, R. M. Hare, J.O. Wisdom, Nicholas Rescher, David Bohm, Paul K. Feyerabend, F. A. Hayek, and Adolf Grunbaum. Social science contributions include Hans Albert on social science and moral philosophy, W. B. Gallie, on the critical philosophy of history, Pieter Geyl on The Open Society and its Enemies, and George H. Nadel on the philosophy of History. (shrink)

Designed to fill a large gap in American philosophy scholarship, this bibliography covers the first four decades of the pragmatic movement. It references most of the philosophical works by the twelve major figures of pragmatism: Charles S. Peirce, William James, John Dewey, George H. Mead, F.C.S. Schiller, Giovanni Papini, Giovanni Vailati, Guiseppe Prezzolini, Mario Calderoni, A.W. Moore, John E. Boodin, and C.I. Lewis. It also includes writings of dozens of minor pragmatic writers, along with those by commentators and critics (...) of pragmatism. It encompasses literature not only concerning pragmatism as an alliance of philosophical theories of meaning, inquiry, belief, knowledge, logic, truth, ontology, value, and morality, but also as an intellectual and cultural force impacting art, literature, education, the social and natural sciences, religion, and politics. This bibliography contains 2,794 main entries and more than 2,000 additional references, organized by year of publication. 2,101 of the references include annotation. Its international scope is focused on writings in English, French, German, and Italian, though many other languages are also represented. Peter H. Hare contributed the Guest Preface. The introduction contains an historical orientation to pragmatism and guides to recent studies of pragmatic figures. This work is extensively cross-referenced, and it has exhaustive and lengthy author and subject indexes. (shrink)

R F Dearden; Education and Politics, Journal of Philosophy of Education, Volume 14, Issue 2, 30 May 2006, Pages 149–156, https://doi.org/10.1111/j.1467-9752.198.

Jung was intrigued from early in his career with coincidences, especially those surprising juxtapositions that scientific rationality could not adequately explain. He discussed these ideas with Albert Einstein before World War I, but first used the term "synchronicity" in a 1930 lecture, in reference to the unusual psychological insights generated from consulting the I Ching. A long correspondence and friendship with the Nobel Prize-winning physicist Wolfgang Pauli stimulated a final, mature statement of Jung's thinking on synchronicity, originally published in 1952 (...) and reproduced here. Together with a wealth of historical and contemporary material, this essay describes an astrological experiment Jung conducted to test his theory. Synchronicity reveals the full extent of Jung's research into a wide range of psychic phenomena. This paperback edition of Jung's classic work includes a new foreword by Sonu Shamdasani, Philemon Professor of Jung History at University College London. (shrink)

The "problem of counterfactuals," as proposed by Goodman and Chisholm, cannot be solved. However, a similar program, pioneered by Hiż and Mrs. Milmed, but largely neglected, can be completed and promises a satisfactory analysis of subjunctive conditionals.

I am concerned with the subject as an ethico-religious problem. Is suicide all right or isn't it; and if it isn't, why not?The question should not be assumed to be susceptible of an answer in the way the question whether arsenic is poisonous is susceptible of an answer. Moreover in the case of arsenic the question what it is, and the question whether it is poisonous, are separable questions: you can know that arsenic is poisonous without having analysed its nature. (...) But to know or believe that suicide is objectionable is to have analysed its nature or construed its significance in one way rather than another. (shrink)

Find out all about dreams and you will know all about insanity. —Hughlings Jackson.